Duality for Lipschitz p-summing operators
Seminar Room 1, Newton Institute
A theorem of J. Bourgain states that any finite metric space can be embedded into a Hilbert space with distortion proportional to the logarithm of the number of points. In fact Bourgain's embedding has a richer structure, that of a Lipschitz p-summing operator. These operators were introduced by J. Farmer and W. B. Johnson, and generalize the concept of a linear p-summing operator between Banach spaces . In this talk we identify the dual of the space of Lipschitz p-summing operators from a fi nite metric space to a normed space, answering a question of Farmer and Johnson. Furthermore, we use it to give a characterization of the non-linear concept of Lipschitz p-summing operator between metric spaces in terms of linear operators between certain Banach spaces.